The Transactions of the Korean Institute of Electrical Engineers D (대한전기학회논문지:시스템및제어부문D)

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지

Design of a Sliding Mode Control with an Adaptation Law for the Upper Bound of the Uncertainties

불확실성의 경계치 적응기법을 가진 슬라이딩 모드 제어기 설계

  • 유동상 (한경대학교 전기공학과)
  • Published : 2003.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

In order to describe the upper bound of the uncertainties without any information of the structure, we assume that the upper bound is represented as a Fredholm integral equation of the first kind, that is, an integral of the product of a predefined kernel with an unknown influence function. Based on the improved Lyapunov function, we propose an adaptation law that is capable of estimating the upper bound and we design a sliding mode control, which controls effectively for uncertain dynamic systems.

Keywords

References

  1. V. I. Utkin, 'Variable structure systems with sliding modes', IEEE Transactions on Automatic Control, vol, 22, no. 2, pp. 212-222, February 1977 https://doi.org/10.1109/TAC.1977.1101446
  2. R. A. DeCarlo, S. H. Zak, and G. P. Matthews, 'Variable structure control of nonlinear multivariable systems: A Tutorial', Proceedings of IEEE, vol. 76, no. 3, pp. 212-232, 1988 https://doi.org/10.1109/5.4400
  3. Y. H. Chen, 'Robust control system design: non-adaptive and adaptive', International Journal of Control, vol, 51, no. 6, pp. 1457-1477, 1990 https://doi.org/10.1080/00207179008934146
  4. D. S. Yoo and M. J. Chung, 'A Variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties', IEEE Transactions on Automatic Control, vol. 37, no. 6, pp. 860-865, June 1992 https://doi.org/10.1109/9.256348
  5. B. Brogliato and A. Trofino Neto, 'Practical stabilization of a class of nonlinear systems with partially known uncertainties', Automatica, vol, 31. no. 1, pp. 145-150, 1995 https://doi.org/10.1016/0005-1098(94)E0050-R
  6. H. Wu, 'Continuous adaptive robust controllers guaranteeing uniform ultimate boundedness for uncertain nonlinear system', International Journal of Control, vol, 72, no. 2, pp. 115-122, January 1999 https://doi.org/10.1080/002071799221280
  7. G. Arfken. Mathematical methods for physicists, Academic Press, New York, pp. 725-748, 1970
  8. W. Messner, R. Horowitz, W.-W. Kao, and M. Boals, 'A New Adaptive Learning Rule', IEEE Transactions on Automatic Control, vol. 36, no. 2, pp. 188-197, February 1991 https://doi.org/10.1109/9.67294
  9. V. M. Popov, Hyperstability of control systems, Springer-Verlag, New York, pp. 210-213, 1973
  10. M. J. Corless and G. Leitman, 'Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems', IEEE Transactions on Automatic Control, vol, 26, no. 5, pp. 1139-1144, May 1981 https://doi.org/10.1109/TAC.1981.1102785
  11. P. A. Ioannou and P. V. Kokotovic, 'Instability analysis and improvement of robustness of adaptive control', Automatica, vol. 20, no. 5, pp. 583-594, 1984 https://doi.org/10.1016/0005-1098(84)90009-8